Random-order fractional differential equation models

Authors:
HongGuang Sun;YangQuan Chen;Wen Chen
Affiliations:
Key Laboratory of Coastal Disasters and Defence of Ministry of Education, Hohai University, Nanjing 210098, China and Center for Self-Organizing and Intelligent Systems (CSOIS), Department of Elec ...;Center for Self-Organizing and Intelligent Systems (CSOIS), Department of Electrical and Computer Engineering, Utah State University, 4160 Old Main Hill, Logan, UT 84322-4160, USA;Institute of Soft Matter Mechanics, Department of Engineering Mechanics, Hohai University, No.1 XiKang Road, Nanjing, Jiangsu 210098, China
Venue:
Signal Processing
Year:
2011

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Abstract

This paper proposes a new concept of random-order fractional differential equation model, in which a noise term is included in the fractional order. We investigate both a random-order anomalous relaxation model and a random-order time fractional anomalous diffusion model to demonstrate the advantages and the distinguishing features of the proposed models. From numerical simulation results, it is observed that the scale parameter and the frequency of the noise play a crucial role in the evolution behaviors of these systems. In addition, some potential applications of the new models are presented.